On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance. (22nd February 2018)

• Record Type: Journal Article
• Authors: Kasumo, Christian; Kasozi, Juma; Kuznetsov, Dmitry
• Other Names: Abbasbandy Saeid Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2018(2018)
• Publication Date: 2018-02-22
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2018/9180780
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : We consider an insurance company whose reserves dynamics follow a diffusion-perturbed risk model. To reduce its risk, the company chooses to reinsure using proportional or excess-of-loss reinsurance. Using the Hamilton-Jacobi-Bellman (HJB) approach, we derive a second-order Volterra integrodifferential equation (VIDE) which we transform into a linear Volterra integral equation (VIE) of the second kind. We then proceed to solve this linear VIE numerically using the block-by-block method for the optimal reinsurance policy that minimizes the ultimate ruin probability for the chosen parameters. Numerical examples with both light- and heavy-tailed distributions are given. The results show that proportional reinsurance increases the survival of the company in both light- and heavy-tailed distributions for the Cramér-Lundberg and diffusion-perturbed models.